water tree detection in underground cables

IEEE Power and Energy Technology Systems Journal

Received 12 June 2014; revised 13 February 2015; accepted 22 March 2015. Date of publication 8 May 2015;date of current version 10 August 2015.

Digital Object Identifier 10.1109/JPETS.2015.2420791

Water Tree Detection in Underground CablesUsing Time Domain Reflectometry

KLAEHN W. BURKES1 (Student Member, IEEE), ELHAM B. MAKRAM2 (Fellow, IEEE),AND RAMTIN HADIDI2,3 (Member, IEEE)

1Savannah River National Laboratory, Aiken, SC 29808-0001 USA2Holcombe Department of Electrical and Computer Engineering, Clemson University, Clemson, SC 29634 USA

3Clemson University Restoration Institute, North Charleston, SC 29405 USA

CORRESPONDING AUTHOR: R. HADIDI ([email protected])

This work was supported by the Clemson University Electric Power Research Association.

ABSTRACT This paper proposes to use time domain reflectometry (TDR) to detect water trees inunderground residential distribution (URD) cables. Water trees are very dangerous to underground cables.They can grow for years without any change on the performance of the cable, and then can cause thecable to fault unexpectedly. Therefore, a method to detect water trees in URD cables is proposed in thispaper. The method implements an optimal pulse generator placement algorithm on a distribution feeder forperforming TDR. It can determine the exact location of a water tree in a cable, and it does not rely on thelength of the cable or the type of cable used. The method can also detect multiple water trees on the samecable, and can be installed on existing systems, since it does not require data of the healthy system. It is aperiodic monitoring systemwhere pulses are sent throughout the year. The proposedmethod has been verifiedusing multiple case studies on a real distribution feeder. Using TDR, optimal pulse generator placement, andsubtraction of cables’ measured signal in time domain with similar measured signals a critical distributionfeeder’s health has been monitored successfully.

INDEX TERMS Time domain reflectometry (TDR), underground residential distribution (URD), water tree.

I. INTRODUCTION

WATER trees are a phenomenon that occur in theinsulation of underground cables. Water trees cannot

be detected by online diagnostic techniques such as partialdischarge tests, mainly because water trees do not producepartial discharges [1], which is why their detection is impor-tant to utility companies. In addition, they grow in cableswithout any effect on the voltage or current [2]. Water treesform in extruded dielectric materials, such as cross linkpolyethylene (XLPE) or ethylene propylene rubber [2]. Theygrow from discontinuities or impurities at the insulation andshield’s interface. These impurities cause the electric fieldto intensify, which then breaks down the insulation, causingmicrofractures. These microfractures fill with moisture andcause the electric field to increase. They will continuallygrow until they reach the conductor. Water trees grow in abush- or tree-like shape. The electric properties inside theellipsoid change from the insulation’s properties, such as itsrelative permittivity or electrical conductivity [3]. It has beenshown that the permittivity and conductivity on the surface

of the ellipsoid is the same as those of the insulation, but itincreases linearly to the initiation point [4]. The permittivitycan increase to three times the insulation’s permittivity [4]and the conductivity can increase to 1010 times theinsulation’s conductivity [5].

Water tree detection is becoming more important nowbecause utility companies are converting their overhead linesto underground cables due to aesthetics. Since utility com-panies are doing this, they need to be able to monitor thehealth of their distribution networks for the reliability andsecurity of the distribution system. Power cables cause themajority of distribution grid failures [6]. However, damage toan underground cable cannot be seen visually like overheadlines. For utilities to be certain of the health of their distribu-tion networks, new methods for monitoring the undergroundresidential distribution (URD) need to be proposed.

There are currently cable health tests available commer-cially. These tests consist of withstand tests, dc currentmeasurement, dissipation factor, and partial discharge [3].However, withstand tests, dc current measurement,

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and dissipation factor are all performed off-line. Therefore,the cable must be disconnected and service interrupted.In addition, the withstand test stresses the cable until failureand the cable is ruined after the test [3]. The dissipationfactor measures the leakage current and monitors the resistiveportion of the current. The resistance current increasing is anindicator that the insulation is breaking down. Furthermore,the dissipation factor is the ratio of resistance currentover capacitive current. However, when the cables’ lengthincreases, the ratio of resistance to capacitance reduces,causing this test to not show any indicator in long cables.In addition, this test does not distinguish between a group ofdeteriorations in the insulation and a single deterioration [3].Partial discharge detection can be performed online and iscapable of detecting partial discharges far away from themeasurement device. However, water trees do not producepartial discharges [2], and only electrical trees producepartial discharges. Therefore, by the time the partial dischargeequipment has detected anything, the cable will be minutesaway from failure [3]. Some research is also looking intousing radio frequency signals to measure dielectric loss andthe change in permittivity of an energized cable’s insulationunder the presence of water trees [7], and should be noted asa method for online detection of water trees.

The use of time domain reflectometry (TDR) to detectwater trees can be performed online, it does not damage thecable, and it can detect water trees years before they will fail.Therefore, TDR is a good onlinemethod tomonitor the healthof URD.

In this paper, the water tree model will be discussed further.Then, a water tree detection method will be presented usingTDR for a water tree in a single cable. Next, a distributionfeeder constituted of underground cables is introduced. Then,an optimal pulse generator placement algorithm is presentedby manipulating an optimal phasor measurement unit (PMU)algorithm. Next, the amplitude of the pulse needed to monitorthe cables in the distribution feeder is determined based oncost of the equipment. Then, an algorithm for monitoring allthe cables in the distribution feeder is constructed, and finally,the results from the cable monitoring algorithm are presentedwith several cases of cable configurations.

II. WATER TREE MODELA finite-element analysis simulation of a water tree in a tapeshield cable was simulated in COMSOL Multiphysics [8],where the effect of the water tree can be seen on the voltageand electric field and is shown in Fig. 1. The explanation ofthe water tree and simulation are reported in [9]. The electricfield is represented by the red arrows and the electric potentialis represented by the surface plot.

This figure shows that the electric field is directed per-pendicularly to the conductor of the cable and is nonexistentoutside of the tape shield. In addition, the electric potentialof the conductor is at 15 kV and reduces linearly until thegrounded tape shield. This agrees with previous researchdone in COMSOL on water trees [10], [11]. Outside of the

FIGURE 1. Water tree 90% across insulation.

tape shield the electric potential is zero. Furthermore, theelectric field is increased at the tip of the water tree, whichallows for the water tree to continue growing. Since the watertree is grounded, it is acting as a conductor and has the samepotential as the tape shield. Additionally, the voltage insidethewater tree is constant and the electric field is perpendicularto its surface. Both of these are due to the water tree acting asa conductor.

The water tree model is a well-known model. Thewater tree is represented as a parallel resistance andcapacitance [3], [12]–[14]. However, the value of resistanceand capacitance is not well-known. Therefore, in order tosimulate the water tree in software, the resistance and capac-itance must be calculated. This was done in COMSOLMultiphysics [8]. A vented water tree was simulated growingfrom the outside of the cable to the conductor. A vented watertree grows from conductor to sheath or sheath to conductor.This was chosen because vented water trees are the mostdangerous type of water tree [3]. The water tree was variedacross the insulation and the resistance and capacitance werecalculated using COMSOL Multiphysics. The capacitance isshown in Fig. 2(a), and the resistance is shown in Fig. 2(b).

FIGURE 2. (a) Capacitance and (b) resistance per millimeter ofcable slice as the water tree grows across the insulation.

From Fig. 2(b), it can be observed that the resistance ofthe water tree segment does not change until the water tree is

54 VOLUME 2, NO. 2, JUNE 2015

Burkes et al.: Water Tree Detection in Underground Cables Using TDR

touching the conductor. Since the water tree is not touchingthe conductor, no resistive current can leak out through thewater tree, and therefore, the resistance is constant.

From the figure, the capacitance has an exponential changewhich is what would be expected. This is due to the water treeacting as a conductor, and as it grows closer to the cable’sconductor, it is increasing the capacitance at that location.

When the shape of the water tree was changed the responseof the capacitance and resistance did not change, but the exactvalue was affected. For the rest of the research, a thin ellipsoidwas used with a width a twelfth of the length.

III. WATER TREE DETECTION METHOD USING TDRTDR works by sending a pulse down a cable andmonitoring for any reflection to return before thetermination pulse returns. The reflections that are seen beforethe termination pulse are due to impedance mismatches in thecable. These impedancemismatches could bewater trees. Thelocation of the water tree is determined from

D =tr × v2

(1)

where tr is the time of the received reflection and v is thevelocity of the wave traveling through the cable. The velocityof the cable is calculated using the same equation on a cablewith a known distance. The cables installed into this systemall have XLPE and their resulting velocity is 2.01×108 ms−1.This is close to the theoretical value of 1.76× 108 ms−1 andthe results of previous research 1.96× 108 ms−1 [15].However, there can be sections of cable that are spliced

together with joints that would send reflection pulse backbefore the termination reflection pulse was measured aswell. These reflection pulses could be mistaken for watertrees. Therefore, the model of a cable joint was constructedusing the research in [16]. The model is represented astwo shunt resistance and capacitance connected together withan inductance.

To compare whether or not the cable joint’s reflectionpulse will be the same as the water tree’s, the characteristicimpedance formula must be known. For an infinitely longline, the characteristic impedance is calculated as follows:

Z0 =V (x)I (x)=

√R+ jωLG+ jωC

. (2)

At high frequencies, the resistance and conductance arenegligible compared with the high frequency inductance andcapacitance. Therefore, the characteristic impedance of acable is represented by the square root of the inductance overthe capacitance as seen in

Z0 '

√LC. (3)

L andC are used in the calculation of the impedance at highfrequencies. For a water tree C = capacitance of water treeand L ≈ 0. For a cable splice C ≈ 0 and L = inductanceof the cable splice. For a segment of cable C = per unit

length capacitance of the cable from conductor to sheath andL = per unit length of inductance of the conductor.

From this equation, it can be determined that when theinductance is increased in the cable, the impedance increasesat that location and it is greater than the characteristicimpedance causing a positive reflection pulse. In addition,when the capacitance is increased in the cable, the impedancedecreases at that location and is less than the characteristicimpedance causing a negative reflection pulse.

Since the cable joint’s lumped parameters are mainlyinductive, as explained above, it should produce a positivereflection pulse. This is due to the fact that the cable jointincreases the impedance at that location. The model of thecable joint in [16] was implemented in PSCAD [17] on asingle phase of the cable. A high frequency pulse was placedon the cable, as shown in Fig. 3(a).

FIGURE 3. Measured signals in cable (a) high frequency pulsesent and (b) reflection wave from water tree and cable splice.

Likewise, the water tree’s lumped parameters are repre-sented as a parallel resistance and capacitance, as statedpreviously. Therefore, there should be a negative reflectionproduced from the water tree. This is because the resistancedoes not have any affect during the high frequency pulse andthe capacitancewould reduce the characteristic impedance, asstated above. The water tree was simulated on a single cableto see the reflection pulse produced. The reflection pulse froma cable splice and a water tree are shown in Fig. 3(b).

The water tree produces a negative reflection pulse, asdetermined above, with a very small magnitude. Likewise,the cable joint produces a positive reflection pulse that isshown in Fig. 3(b). Since the water tree’s size is micro-scopic and the size of the cable joint is around a foot, thereflection magnitude of the water tree is much smaller thanthe reflection magnitude of the cable joint. A study of thetwo characteristics, amplitude and reflection direction, allowsfor distinguishing between a water tree and a cable joint.Therefore, water trees can be detected by TDR and not beconfused with a cable joint.

IV. DISTRIBUTION FEEDERThe statement that TDR can detect water trees was proved,as demonstrated in this paper. However, the next step is to

VOLUME 2, NO. 2, JUNE 2015 55


FIGURE 4. One-line diagram of distribution feeder.

determine if it can monitor the health of the cables in adistribution feeder. Therefore, a real distribution feeder wasused for practicality. The distribution feeder is located alongthe coast of the Carolinas and it consists of mainly three phaseloads. These loads are commercial loads, including hotels,restaurants, and shops. These businesses are vital customersfor the utility company. Another reason that a real distribu-tion feeder was used is the fact that the distribution feederconfiguration can be quite complex and studying a testcase or IEEE system would not provide enough complexity.All the information was given by a local utility, and is givenin [18]. A one-line diagram of the distribution feeder is givenin Fig. 4. There are 29 buses, 54 loads, and 78 cables.

V. OPTIMAL PULSE GENERATOR PLACEMENTIt is not financially feasible to place a pulse generator onevery bus in a distribution feeder. Therefore, an optimalpulse generator placement scheme must be used to determinethe location for pulse generators in the system. This opti-mal pulse generator scheme is very similar to optimalPMU placement because it allows for full observation of thesystem. Therefore, themethod of optimal placement of PMUsby integer linear programming proposed in [19] and [20]will be used for determining the optimal location for thepulse generators placement in the distribution feeder. Theoptimal PMU placement algorithm uses the y-bus matrix toimplement this programming technique where all nonzerovalues are set to 1. However, this does not consider the factthat some buses are not connected to any underground cablesand do not need to be part of the optimization. Therefore,this method needs to be modified and a new y-bus should becreated, wherein a 1 in the diagonal row means that the bus isconnected to a cable

yi,j =

1, if i = j and bus is connected to a cable1, if i and j are connected by a cable0, otherwise.

(4)

For the buses not connected to a cable, a 0 is insertedinto the diagonal row. For the elements not in the diagonal,a 1 represents the buses that are connected togetherthrough cables, and a 0 means there is no connection

or they are connected by overhead lines. This is statedin (4) above.

The optimal placement of pulse generators is formulatedas follows [19]:

Minn∑i=1

xi

s.t. Ypulse × X ≥ b

X = [x1, x2, . . . , xn]

xi ∈ {0, 1}

b = [b1, b2, . . . , bn]. (5)

In this equation, n is the number of buses, xi represents eachbus, and bi is equal to 1 if the bus is connected to cables,or 0 if it is not connected to any cables. Ypulse is the y-buscreated previously. The program minimizes the number ofbuses with pulse generators so that buses connected toeach other through cables will have at least one pulsegenerator. The integer linear programming method proposedthat seven of the 23 Buses connected to underground cablesshould have a pulse generator installed in order to minimizecost and allow for adequate monitoring of the health of all thecables, as shown in Table 1.

TABLE 1. Results from optimization.

A 1 in results rows means a pulse generator should beadded to the bus, and a 0 represents no pulse generator. Thetable’s columns are highlighted in different colors to representwhat groups of buses are being monitored by the differentpulse generators. As it can be seen, some buses are connecteddirectly, or from a short distance, to multiple buses and canmonitor three to four other buses, such as Bus 24 and Bus 17.There are also buses that only monitor themselves, such asBus 13, or just one adjacent bus, such as Bus 22. This is



simply due to the nature of this individual distribution feeder.For example, Bus 13 has a single cable connected to it but isnot connected to any other bus through a cable. Instead, it isconnected to other buses with overhead lines. Therefore,if all three phase cables in the distribution feeder are to bemonitored, then a pulse generator must be placed on Bus 13even though it can only monitor one cable. Furthermore,Bus 22 is connected in between Bus 24 and Bus 20 throughseveral cables in series with loads in between them andBus 20is directly connected to Bus 24 and Bus 17. Therefore, Bus 22can only monitor Bus 21 and the cables directly connected toBus 22 and Bus 21. However, this pulse generator is neededsince Bus 24 cannot monitor Bus 21 because it is too faraway. From Table I, it can be seen that there is a groupof buses connected to the main system by overhead lines:Buses 5, 6, 7, and 8. If these buses are not supplying veryimportant loads then they might not need to be monitored,thereby reducing the cost. However, they are monitored in thesimulation to prove that all cables can be monitored.

VI. PULSE GENERATORThe pulse generator used must have a fast rise time in orderto monitor the health of very short cables. This is due tothe fact that distribution feeders consist of very short cablesconnecting longer cables to each other and to the load.The pulse generator should be able to detect water trees incables >10 ft. The reason a length of 10 ft was picked isthat in the simulated distribution feeder, the smallest cableis 12-ft long and therefore 10 ft was picked as the shortestlength. A cable 10-ft long will see its reflection after∼30 ns.Therefore, the pulse generator needs to have a rise time of1 ns or less and a pulsewidth of <5 ns to be able to monitorcables as small as 10 ft, as seen in Fig. 5.

FIGURE 5. Generated pulse and termination reflection pulsein 10-ft cable.

The pulse generator’s amplitude will determine the priceof the pulse generator. Therefore, a study of the size ofthe pulse needed to detect the water tree was performed.Two pulse generators were studied. One, a 240 V 1-ns risetime pulse generator and the other, a 5 kV 0.1-ns rise timepulse generator. These two pulse generators are very differentin amplitude, and therefore, the extreme cases can bestudied. The two pulse generators were inputted into on

a 100-ft long cable. The reflection waves from the water treefor the two different simulations are shown in Fig. 6.

FIGURE 6. Water tree pulses for 240 V and 5-kV pulse generatorin 100-ft cable.

As it can be seen in Fig. 6, the voltage pulse of the watertree is not significantly increased. It is only increased by afactor of four. Further studies were performed on differentlengths of cables to see if the length of the cable made adifference, as shown in Table 2.

TABLE 2. Reflected pulse amplitude ratio.

For cables smaller than 100 ft, the difference in the watertree’s reflected pulse was much greater, making the highervoltage pulse generator worth using. An example of thiswould be the 50-ft cable, where the 5-kV pulse generator’swater tree reflected pulse had a magnitude >12 timesthe 240 V pulse generator. However, the average length forthe cables in the distribution feeder used is 250 ft, and thebreakdown of cable lengths is shown in Table 3.The maximum number of cables is between 100 and 200 ftand the percentage of the cables above 100-ft long is 76.9%.

TABLE 3. Breakdown of cable lengths.

Prices were found for the pulse generators with thoseproperties. They are shown in Table 4.

TABLE 4. Prices for pulse generators in 2014.



The price for the high-voltage pulse generator isthree times the price of the low-voltage pulse generator.Therefore, the total cost of implementing a TDR water treemonitoring system with a 5-kV pulse generator would bethree times more than a system with a 240 V pulse generator.For this distribution feeder, with 76.9% of its cables beinglonger than 100 ft, it is proposed to use the low-voltage pulsegenerator to save money. However, this decision was madewithout knowing the importance of the loads being suppliedby the cables. For high-priority loads connected through ashort cable, a high-voltage pulse generator should be placed atthat bus only, and the rest of the buses could have low-voltagepulse generators connected to them. This would increasesecurity with minimal cost.

VII. CABLE MONITORING ALGORITHMFOR A DISTRIBUTION FEEDERWith the pulse generators in place, the next step is todetermine which cables will be monitored by each pulsegenerator. This is done by firing each pulse generatorindividually and sending a pulse for each phase individuallyat the zero crossing of each phase. In addition, it should benoted that this is not taking place every cycle and is not areal-time monitoring method. However, theses pulses wouldbe sent quarterly each year and the information stored formonitoring. In addition, if a water tree pulse is found, thecable will not get immediately removed due to the fact thatwater trees grow very slowly and take years to cause cablefaults. However, the size of the water tree can be monitoredfrom the size of the reflected pulse. This can be used todetermine when the cable should be replaced.

First, if the cable is connected directly to the bus the pulsegenerator is connected to, the cable can be monitored andthe water tree detected. Therefore, every cable connectedto the bus which the pulse generator is connected to canbe monitored directly. This will be shown in Case Study Ain Section VIII.

Cables that are connected to the pulse generator busthrough multiple cables cannot be monitored directly. Thisis due to the fact that other cables’ reflections will betransmitted into the monitored cable. These will occurbefore the monitored cable’s termination reflection is seen.Therefore, to remove these reflections from the moni-tored cable’s signal, a cable’s signal connected at thesame bus is subtracted from the monitored cable’s signal.This is done because the two cables will have the sametype of disturbances on their measured signal, and thesedisturbances can be removed by subtracting the cables.Therefore, the two cables’ signals will be subtracted fromeach other and they can now be monitored and watertrees can be detected. This is shown in Case Study Bin Section VIII.

If there are no two cables connected, as mentioned before,but there is a single-phase cable connected to one of thephases of the monitored cable, the single-phase cable’s pulsecan be monitored. Then, its pulse can be stored and is

subtracted from each phase. Therefore, each phase of thethree-phase cable can be monitored at the junction.

However, if there is a load connected instead of a single-phase cable, there is nothing to subtract from the cable signal.Therefore, in order to monitor that cable, a pulse should besent from a generator on the other side of the cable. Instead ofbeing fed the pulse through a cable, it now may be connectedto a bus with another cable for subtraction as described above,and the cable’s health can be monitored. This was done forCase Study C in Section VIII. Finally, if there are two cablesconnected to a bus, which is connected to the bus with apulse generator through multiple cables, this method can stillmonitor the health of the cables. This is also seen in CaseStudy C in Section VIII.

However, if there is no single-phase cable but there is aload, there is still a method to detect the water trees in thecable. Each signal from all three phases will be stored andsubtracted from each other. This method will work becausethree-phase cables are bundled together in conduit. Therefore,either the water tree is initiated through some protrusionin a single cable or there is some defect that causes twowater trees to form in two cables at the same location. Thus,if the two signals were subtracted from each other they wouldremove the water tree pulse. However, the third phase wouldnot have a water tree in this location. Therefore, when thissignal is subtracted from both of the water treed phase signals,the water trees in the other two phases could be detected,as seen in Case Study D in Section VIII.

VIII. CASE STUDIESWater trees were placed on every cable as lumped parametersin the distribution feeder to determine if this method allowsfor full observation of the system. The values for the lumpedparameter are taken from Fig. 2 when the water tree is 50%across the insulation [8]. The pulse generators were alsoadded to the system. The types of sensor which can be usedhave been discussed in [6] and are placed at the beginning ofeach cable, where the cable is connected to the bus. The watertree percent distance is the distance from the end of the cableand sensor. Water trees were placed at different percentagesof the length of each cable in order to be certain that thewater tree can be detected at any location along a cable. Then,a series of test was performed. Each pulse generator wasactivated individually in order to not have pulses from othergenerators affect the measured signal. Therefore, seven casestudies were performed, one for each bus.

A. CABLE IS CONNECTED DIRECTLYTO PULSE GENERATOR BUSThe water tree can be detected in the cables that are directlyconnected to the bus with the pulse generator. The value ofthe water tree’s reflected pulse for cables connected to thepulse generator was a magnitude of 10−1 to 10−2 V. Cable 1is 622-ft long and the water tree is located at 5% down thelength of the cable. The cable is connected to Bus 6 directly,and its reflection pulse should return in 1.89 µs. Cable 1’smeasured pulse is located in Fig. 7.



FIGURE 7. Signal sent in Cable 1 connected directly to the pulsegenerator bus.

It can be seen in the figure that the reflected pulse is at amagnitude of 4 V and the water tree’s reflection can be seenwhen zoomed in on the reflected signal. A zoomed-in-viewplot of the water tree reflection pulse is shown in Fig. 8.

FIGURE 8. Water tree pulse on Cable 1 connected to pulsegenerator (zoomed-in-view of window).

From the figure, the water tree’s reflection pulse is∼0.6 V,which can be filtered from noise and detected with simplesensors. The distance of the water tree from the sending endis 31.14 ft and its arrival time is 94.6 ns. The other cablesthat are connected to the pulse generator bus are similar andtherefore the water tree can be detected in cables that aredirectly connected to the pulse generator bus.

B. SUBTRACTION OF CABLES’ MEASURED SIGNALIN TIME DOMAIN CONNECTED TO PULSEGENERATOR BUS THROUGH A CABLEEven though the cables’ health directly connected to the pulsegenerator bus can be monitored, cables that were connectedto the bus with a pulse generator through another cable couldnot directly measure water trees. This was due to the fact thatreflections from other cables in the systemwould cause pulsesthat affected the detection of the water tree. Therefore, if thereare two cables which are connected to the pulse generator bythe same cable, these two cables will be subject to the samepulses that affect detecting the water tree. Cables 2 and 3are connected through the same cables to Bus 28. Cable 2is 78-ft long and a water tree is located 40% from the sendingend. Cable 3 is 222.6-ft long and a water tree is located 80%

from the sending end. The cable signals before subtractionare shown in Fig. 9.

FIGURE 9. Cable signals before subtraction of cablesignals 2 and 3.

As it can be seen, there is no possible way to determineif there is a water tree in the two cables. However, theirsignals have similar values except in specific places. Becauseof this, the signals were subtracted from each other and thenwater trees were capable of being detected in both cables.This is shown in Fig. 10. The refection time for Cable 2’swater tree is 1.15 µs, and the refection time for Cable 3’swater tree is 1.595 µs. In addition, the reflection time forCable 2’s termination is 1.29 µs, and the reflection time forCable 3’s termination is 1.73 µs. These reflections can beseen in Fig. 10.

FIGURE 10. Water trees in Cables 2 and 3 after subtraction ofcables’ signal in time domain.

It can be seen in Fig. 10 that this method will produce apositive water tree reflection pulse in the cable that does nothave a water tree due to the subtraction of the negative watertree pulse from the cable that does. This could bemistaken fora cable joint, but the location of a cable joint should be known.However, if it is not known, the magnitude of the reflectedsignal of a cable joint is much greater than the water tree,as seen in Fig. 3(b).

Therefore, if there is an unknown cable joint on the cableit can be determined whether this reflection is due to thesubtraction of the cable with a water tree or a cable joint.This method is capable of detecting water trees on cablesthat are not the same length, and the water tree can still



be monitored after the smallest cable’s reflected pulse hasreturned. The magnitude of the subtracted cables’ water treeis from 10−3 to 10−2 V as seen in Fig. 10 and can be detectedby sensors.

C. WATER TREE CONNECTED TO PULSE GENERATORTHROUGH MULTIPLE CABLESWhen a secondary cable is connected to the pulse genera-tor through multiple cables, it will receive the same out ofphase voltage pulses as the cables connected to it. Cable 4 is63.76-ft long, and a water tree is located 10% from thesending end. It is connected to Bus 17 by four cables; threecables are connected to Bus 16, and then Cable 4 is connectedto Bus 16 through one cable. Therefore, Cable 4 will receivepulses from these three cables at different times, which are at0.339, 0.372, and 0.708µs. These times depend on the lengthof the cables. The reflection time for the termination signalsare 0.533, 0.566, and 0.901. Therefore, the first two pulseswill be seen before the third pulse arrives and are the focus ofthis paper, and they are shown in Fig. 11.

FIGURE 11. Multiple sent pulses in Cable 4 due to multiple cables.

After subtracting the signal in Fig. 11 as stated in Case B,the sent pulses will cause two water tree reflections to bepresent. The first water tree’s reflection time is 0.358 µs, andthe second water tree’s reflection time is 0.392 µs, as seenin Fig. 12.

FIGURE 12. Water tree reflection pulses in Cable 4 due tomultiple sent pulses.

As it can be seen, the water tree reflection pulse has thesame duration between them as the sent pulses. This will

not indicate multiple water trees. The time difference of themultiple pulses is known. Therefore, it can be verified thatthese water tree reflections are from one water tree due to themultiple pulses.

D. CABLES WITH THREE-PHASESUBTRACTION DETECTIONThe cables that cannot be monitored by the subtractionmethod would then have each three-phase signal stored.Then, they should be subtracted from each other like pre-viously stated. This is simulated by placing water trees onphases A and C of Cable 5. Cable 5 is 226.3-ft long anda water tree is located 30% from the sending end on bothphase A and phase C. The water tree’s reflection time is1.598 µs. The time at which the sending end pulse arrives isat 1.392 µs, and the termination’s reflection time is 2.07 µs.The individual signals for each phase are located in Fig. 13.

FIGURE 13. All three phases of Cable 5 before subtraction.

It can be seen that there is not any difference in the signalsfor each phase. Therefore, the phases could be subtractedfrom each other. The subtraction of phases A and C is shownin Fig. 14.

FIGURE 14. Subtracted signals for phases A and C of Cable 5.

There are some small fluctuations in the signal in-betweenthe sending pulse and the reflection pulse, but nothing withthe same shape as the water tree pulse. This is because bothof these cables have the same size water tree at the samelocation. Figs. 15 and 16 show when phase B is subtractedfrom phases C and A, respectively.



FIGURE 15. Phases C and B subtraction signals of Cable 5.

FIGURE 16. Phases A and B subtraction signals of Cable 5.

The plot where phase B is subtracted from phase A or Cis shown in red above and it can be seen that the water treecan be detected in both phases A and C. It can be verifiedthat the water tree pulses should be present at the same time,which can help with detection. The water tree pulse was largeenough to be detected by sensors and the three-phase subtrac-tionmethodworks tomonitor cables that cannot bemonitoredusing the previously determined subtraction method.

IX. CONCLUSIONAn online noninvasive monitoring scheme for URD cableshas been proposed. It does not rely on the length of the cableor the type of cable used. The proposedmethod can determinethe exact location on the cable that the water tree is located,and multiple water trees can be detected on the same cable.Furthermore, water trees can be detected in cables that areunequal in length. In addition, the proposed method can beinstalled on aged distribution feeders due to the fact that itdoes not require the knowledge of the healthy system as areference unlike previous monitoring methods. The pulseswould be sent periodically throughout the year to monitorthe health of the cables. The signals will all be collected andprocessed through a computer to filter noise and perform thesubtractions. It is not a real-time monitoring system but aperiodic monitoring system, and has been verified using dif-ferent case studies in a real distribution system. The proposedmethod of using TDR, optimal pulse generator placement,and subtraction of cables’ measured signal in time domainwith similar measured pulses is an inexpensive way to moni-tor the health of critical distribution feeders.

ACKNOWLEDGMENTThe authors would like to thank G. Turbeville for providingthe data for the case study.

REFERENCES[1] J. Densley, ‘‘Ageing mechanisms and diagnostics for power cables—

An overview,’’ IEEE Elect. Insul. Mag., vol. 17, no. 1, pp. 14–22,Jan./Feb. 2001.

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KLAEHN W. BURKES (S’12) received theB.S. degree in electrical engineering and theM.S. degree in power systems from Clemson Uni-versity, Clemson, SC, USA, in 2012 and 2014,respectively.

He was a Graduate Research Assistant withthe Holcombe Department of Electrical andComputer Engineering, Clemson University. He iscurrently a Research Engineer with the SavannahRiver National Laboratory, Aiken, SC, USA. His

current research interests include underground residential distribution cables,distributed renewable generation, power hardware in the loop, and dataacquisition.

ELHAM B. MAKRAM (SM’82–F’05) receivedthe M.S. and Ph.D. degrees from Iowa StateUniversity, Ames, IA, USA, in 1978 and 1981,respectively.

She has 11 years of industrial experience asan engineer in power system planning, includingfour years with Seimens, Raleigh, NC, USA, andseven years working in Assiut, Egypt. She joinedClemson University, Clemson, SC, USA, in 1985.She is currently a South Carolina Distinguished

Professor of Power Engineering with the Holcombe Department of Elec-trical and Computer Engineering, Clemson University. She has publishednumerous technical papers on modeling and simulation of machines andtransformers, fault analysis, renewable energy resources, power system edu-cation, and power system analysis (balanced and unbalanced) in the presenceof harmonics and distortion.

Dr. Makram is a member of the American Society for EngineeringEducation, the International Council on Large Electric Systems, andSigma Xi. She is a Registered Professional Engineer in the state ofSouth Carolina.

RAMTIN HADIDI (S’08–M’12) received theB.S. degree from the K. N. Toosi University ofTechnology, Tehran, Iran, the M.S. degree fromthe Iran University of Science and Technology,Tehran, Iran, and the Ph.D. degree from theMemo-rial University of Newfoundland, St. John’s, NL,Canada, in 2012, all in electrical engineering.

He is currently a Research Assistant Profes-sor with the Duke Energy Electric Grid ResearchInnovation and Development Center, Clemson

University Restoration Institute, North Charleston, SC, USA, and theHolcombe Department of Electrical and Computer Engineering, ClemsonUniversity, North Charleston, SC, USA. His current research interestsinclude power system stability analysis and control, renewable energy gridintegration, and computational intelligence and multiagent applications topower systems.

Dr. Hadidi was a recipient of the Khwarizmi International Award in 2009.


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